In meshless natural neighbour Petrov-Galerkin method, the natural neighbour interpolation is used as trial function and a weak form over the local polygonal sub-domains constructed by Delaunay triangulars is used to obtain the discretized system of equilibrium equations. It is a new truly meshless method because no background cells are needed for domain integration. The natural neighbour interpolants are strictly linear between adjacent nodes on the boundary of the convex hull, which facilitates the imposition of essential boundary conditions with ease as it is in the conventional finite element method. The system stiffness matrix in the present method is banded and sparse. The present method for solving stable heat conduction problem is presented and the numerical results show that the present method is quite accurate and stable.